Unit One Patterns and Relations What Youll Learn

Unit One: Patterns and Relations

What You’ll Learn. . . �Use patterns to explore divisibility rules. �Translate between patterns and equivalent linear relations. �Evaluate algebraic expressions by substitution. �Represent linear relations in tables and graphs. �Solve simple equations, then verify the solutions.

Try this problem. . . �Students in grade 7 were raising money for charity. Some students had a “bowl-a-thon”. �This table shows the money that one student raised for different bowling times. Time (hours) Money Raised ($) 1 8 2 16 3 24 4 32 5 40 6 48 1) What patterns do you see? 2) Extend the table. For how long would the student have to bowl to raise $72.

Divisibility Rules �You can use patterns to determine when a number is divisible by a number between 1 -10. �There are no secrets, but, you need to know your times table very well. �You also need to understand what a factor is and how to use factors to your advantage.

�Divisibility Rules help you find the factors of a number quickly. �For example: �What are the factors of 25? �What are the factors of 24?

DIVISIBILITY RULES Number Rule 2 3 4 If the number is even If the sum of the digits is divisible by 3 If the number represented by the last 2 digits is divisible by 4 5 6 8 If the ones digit is 0 or 5 If the number is divisible by 2 AND 3 If the number represented by the last 3 digits is divisible by 8 If the sum of the digits is divisible by 9 If the ones digit is 0 9 10

Divisible by 2 �A number is divisible by 2 if the number is even. All multiples of 2 are even numbers. �Write down 3 numbers that end with an even number. �Check to see if it is divisible by 2 by using long division.

Divisible by 4 � A number is divisible by 4 if the last two digits are divisible by 4. � So, to find out if 352 is divisible by 4, check the last two digits. � 52÷ 4 = 13 � Therefore, 52 is divisible by 4 so, 352 is also divisible by 4. � Would 4052 be divisible by 4?

Divisible by 5 �A number is divisible by 5 if the ones digit is a 0 or a 5. �Some multiples of 5 are: 5, 10, 15, 20 etc. �Write down 3 examples of a number divisible by 5. �Check to see if they are divisible by 5 by using long division.

Divisible by 8 � To check if a number is divisible by 8 check the last three numbers. � Is 1192 divisible by 8? Check 192. � 192÷ 8 = 24 � 192 is divisible by 8, therefore, 1192 is also divisible by 8. � All multiples of 1000 are divisible by 8. So any four digit number only needs the last three numbers checked!

Divisible by 10 �A number is divisible by 10 if the ones digit is 0. All multiples of 10 are divisible by 10. � 30, 70 and 360 are all divisible by 10. �Write down 3 examples of numbers that are divisible by 10 and verify using long division.

FACTORS �To factor means that you write something as a product. Example: 20 = 2 x 5, or 4 x 5 or 10 x 2 �You can set up the factors into a factor tree or chart. You will get a factor chart later today to practice factoring. �But, now, take your hundred chart labeled 301 - 400.

� You need three different colored markers or colored pencils. � Circle all the numbers that are divisible by 2 with one color. � Then, use a different color and circle all the numbers that are divisible by 4. � Then, use third color and circle all the numbers that are divisible by 8. � Choose three numbers greater that 400. Which numbers would be divisible by 2, 4 and/or 8?

�What patterns do you see? �A number that is divisible by 8 is always divisible by 2 and 4 as well. �Why? �Because, 2 x 4 = 8. Therefore, a number divisible by 8 will ALWAYS be even.

Put the following numbers into the Venn Diagram. . . 12, 24, 35, 56, 80, 90, 128, 765, 1048, 1482, 3960, 15019 Divisible by 8 Divisible by 5

Today’s homework. . . �Textbook: Page 8 -9 #1, 2, 3, 4 and reflect �Workbook: Lesson 1. 1